Cheap Hotels in China are easy enough to find once you are in China the problem is trying to find them on the internet . Most of the really cheap hotels in China especially in the smaller cities like Xian and Lasa is very hard as they don't have emails. A discount hotel in China is usually a 2 or 3 star and are reasonable comfortable usually around 35 to 45 USD more or less If you travel in the off season most of the discount hotels will come down to the 25 to 35 USD range roughly 200 Yuan to 250 Yuan
Lhasa Coming to Lhasa with out a reservation can be a bit scary there are some hotels here that you would probably be stuck with and not very happy but we did find a few cheap hotels in Lhasa that I think you will like
Yaks More of a budget hotel in the off season was only 150 Yuan and we did not need to bargain for it nice setup only 10 minutes walking from the Potala Palace the landmark in Lhasa. The Yak has over 100 rooms and is building more they have a hostel like setup for some rooms as well that are only 100 Yuan a night during the high season expect the Yak to cost 450 yuan for a single occupancy.
Mandala hotel is a great choice for a cheap hotel in lhasa at 168 Yuan which is very close to $20 USD anytime of the year this is right next to a landmark.